Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
import java.awt.*;
public class FunkyNumbers
{
    static final int INF = Integer.MAX_VALUE;
    static final int NINF = Integer.MIN_VALUE;
   
    public static void main(String[]args)throws IOException
    {
        Input in = new Input();
        int n = in.nextInt();
        ArrayList<Integer> tris = new ArrayList<Integer>();
        int i = 1;
        while(i*(i+1)/2 <= 1000000000)
        {
            tris.add(i*(i+1)/2);
            i++;
        }

        Integer [] arr = tris.toArray(new Integer[0]);

        for(i = 0; i < arr.length; i++)
        {
            if(Arrays.binarySearch(arr, n-arr[i]) >= 0)
            {
                System.out.println("YES");
                exit();
            }
        }
        System.out.println("NO");
    }

    public static void exit()
    {
        System.exit(0);
    }
}

class Input
{
    BufferedReader br;
    StringTokenizer st;

    public Input()
    {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String nextLine()throws IOException
    {
        StringBuilder sb = new StringBuilder();
        if(st == null)
            st = new StringTokenizer(br.readLine());
        if(!st.hasMoreTokens())
        {
            st = new StringTokenizer(br.readLine());
            return "";
        }

        while(st.hasMoreTokens())
        {
            sb = sb.append(st.nextToken());
            if(st.hasMoreTokens())
              sb = sb.append(" ");
        }
        st = new StringTokenizer(br.readLine());
        return sb.toString();
    }

    public int nextInt()throws IOException
    {
        return Integer.parseInt(next());
    }

    public long nextLong()throws IOException
    {
        return Long.parseLong(next());
    }

    public float nextFloat()throws IOException
    {
        return Float.parseFloat(next());
    }

    public double nextDouble()throws IOException
    {
        return Double.parseDouble(next());
    }

    public String next()throws IOException
    {
        if(st == null || !st.hasMoreTokens())
          st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}